Q. Let P = QQQ be a 3-digit number. What is the HCF of P and 481?
(a) 1
(b) 13
(c) 37
(d) 481
Correct Answer : (c) 37
UPSC Prelims 2025 CSAT
Explanation :
1. Express P in terms of Q:
P = QQQ = 100·Q + 10·Q + Q = 111·Q
2. Factor 111 and 481:
111 = 3 × 37
481 ÷ 13 = 37, so 481 = 13 × 37
3. Compute HCF(P, 481):
HCF(P, 481) = gcd(111·Q, 481)
= gcd(3·37·Q, 13·37)
= 37 · gcd(3.Q, 13)
Since Q is a digit 1–9, 13 does not divide 3Q, so gcd(3.Q, 13) = 1.
Therefore HCF(P, 481) = 37.
Answer: (c) 37
